Quantitative Aptitude Prep Tips for MBA

How many pairs of positive integers x, y satisfy $\frac{1}{x} + \frac{6}{y} = \frac{1}{15}$ , where y is a two digit odd integer?

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Contributor-Level 10

$\frac{1}{x} = \frac{1}{15} - \frac{6}{y}$

$\frac{1}{x} = \frac{y - 90}{15 y}$

$x = \frac{15 y}{y - 90}$ ______equation 1

i.e. y = 90+y,

1≤ y₁ ≤9

y₁ is odd

Equation 1 becomes

$x = \frac{15 (90 + y_{1})}{y_{1}}$

$= 15 + \frac{90 * 15}{y_{1}}$

y₁ can take 1,3,5,9

y=91, 93, 95, 99

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a month ago

An alcohol solution is formed by mixing two solutions. Solution 1 had a concentration of 20 percent and a volume of 3L while solution 2 had a concentration of 40 percent with a volume of 1L. The resultant solution was named solution 3. Three litres of solution 4 which had an unknown concentration was mixed with solution 3. What must be concentration of solution 4 if that the new resultant solution has a concentration of 50 percent?

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Contributor-Level 10

Sol1	20percent (0.6)	3L
Sol2	40percent (0.4)	1L
Sol3	1L	4L
Sol4	XL	3L
Sol5	3.5L	7L

1 + x = 3.5

x= 2.5

Required percent y = $\frac{2.5}{3} * 100$ = 83.33 percent

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a month ago

Two geometric means a, b are inserted between x and y such that a³+ b³ = n (ab) A,where A is the arithmetic mean of x and y. What is value of n?

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Contributor-Level 10

x, a, b, y are in GP

a = xr

b = xr²

y = xr³

r = ${(\frac{y}{x})}^{1 / 3}$

rewrite,

a = x^2/3.y^1/3

b = x^1/3.y^2/3

a * b = x * y

a³+ b³= x²y + y² x

= xy (x+y)

= xy (2A) …………… $[\frac{x + y}{2} = A]$

Hence, n = 2

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a month ago

A square with maximum possible length of the side is inscribed in an equilateral triangle and a circle of maximum possible radius is inscribed in the square. Find the ratio of the length of equilateral of the equilateral triangle to the radius of circle.

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Contributor-Level 10

Let the side of = a

CD = a/2

Let EC = x

In GEC

GE/EC = tan60 = $\sqrt[]{3}$

GE = x $\sqrt[]{3}$

DE = a/2 – x = FG = HF

GE = HG

$x \sqrt[]{3} = \frac{a}{2} - x + \frac{a}{2} - x$

x $\sqrt[]{3}$ = a – 2x

x = $\frac{a}{\sqrt[]{3} + 2}$

GE = x $\sqrt[]{3}$ = $\frac{a \sqrt[]{3}}{\sqrt[]{3} + 2}$

r = side of square ÷ 2

r= $\frac{a \sqrt[]{3}}{4 + 2 \sqrt[]{3}}$

ratio = a/r

= $\frac{a (4 + 2 \sqrt[]{3})}{a \sqrt[]{3}}$

= $\frac{4 + 2 \sqrt[]{3})}{\sqrt[]{3}} = \frac{4}{\sqrt[]{3}} + 2$

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a month ago

A certain sum of money invested at CI becomes Rs 3380 in 2 years & Rs 3515.20 in 3 years. What is the sum invested & what is rate % per annum?

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Contributor-Level 10

(d):3515.2 – 3380 = 135.2 = SI on Rs. 3380 for one year.

By SI formula, 135.2 = $3380 * R * \frac{1}{100}$ $\frac{}{}$ or R = 4 %

Now we have 3380 = P (1.04)2 or P = Rs. 3125

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a month ago

Duronto Express in motion, 66 metre long overtakes a passenger train 88 metres long travelling at 30 kmph in the opposite direction in 0.168 minute. Find speed of the Duronto Express.

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Contributor-Level 10

(c):Let speed of passenger train be x m/s.

$[(\frac{66 + 88}{8.33 + x})] = 0.168 * 60$

$[30 * \frac{5}{18} = 8.33]$

x = 6.94 m/sec = 25 kmph.

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a month ago

A 10 floor building is build by 2 men, 3 women and 4 boys in 10 days. If a man, a women & a boy work in the ratio 5 : 4 : 2. Find the time that 6 men, 4 women and 7 boys take to build a 16 floor building.

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Contributor-Level 10

(c):We have 4 men = 5 women 1 man = $\frac{5}{4}$ $\frac{}{}$ women, 2 women = 4 boys, 1 women = 2 boys $\frac{5}{4}$ $\frac{}{}$ women = 2 * $\frac{5}{4}$ $\frac{}{}$ boys = $\frac{5}{2}$ $\frac{}{}$ or 1 man = $\frac{5}{4}$ $\frac{}{}$ women = $\frac{3}{2}$ $\frac{}{}$ boys

Now 2M + 3W+ 4B = 2 * B + 3 * 2B + 4B = 15 B Boys

Or 15 Boys do the work in 10 days (10 hectares) 6M + 4W + 7B = (6 * + 4 * 2 + 7) B = 30

Boys 30 boys will do 16 hectares of work in 8 days.

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a month ago

During the months of October Krishna went to a temple every day. He offered 4 flowers to her favourite deity. At the end of the month, he noticed that he did not offer the same combination of flowers on any two days during the month. What is the minimum number of varieties of flowers offered by Krishna during the month?

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Contributor-Level 10

Let he offered 'n' different flowers

October has 31 days

ⁿC₄ ³ 31

Minimum value of n can take 7

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a month ago

The ratio of the number of men to women in a class is 5 : 3. On dividing certain number of cookies such that each student got the same number of cookies, the teacher was always left with two cookies. Which among the following cannot be the number of cookies that the teacher had?

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Contributor-Level 10

(c):When the number of cookies was divided into 8 parts or multiples of 8 parts, 2 were always left. So the number of cookies must be a multiple of 8 + 2. Only 17 is not such a value

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a month ago

In a quiz, six team with two member one man and one woman each participated. During dinner all the 12 members were seated around a round table. Find the probability that no man sat to the left of the woman from this team, provided that men and women were alternatively seated.

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